可控源电场数据三维反演及应用

发布时间：2018-08-31 13:10

【摘要】：可控源音频大地电磁测深法(CSAMT)自上世纪七、八十年代问世以来，已经发展成为一种重要的电磁法勘探手段。现在，可控源方法的一维、二维的正反演研究已日趋成熟，三维正反演研究也已有了长足的进步。常用的正演算法有有限差分法、有限元法和积分方程法，反演方法有共轭梯度法、非线性共轭梯度法、牛顿法、拟牛顿法等。但由于计算量非常大，占用内存空间多等的限制，距离实际应用还有一定距离。因此本文期望在现有的技术的基础上，考虑反演过程中如何选择初始模型和频率，期望通过大量的数值模拟，提出在满足①节约计算量②提高反演速度③不牺牲反演效果的条件下，可控源实际应用的一种解决方案，实现高效的三维实际数据反演。首先，正演理论上我们借鉴了Commer等的思路，将有限长导线源激发的总电场，分解为由层状介质电阻率产生的背景场和三维异常体产生的异常场。背景场计算采用虚界面法，数值计算上用直接积分法。异常场计算采用的是交错网格有限差分法。反演方面，本文利用了拟牛顿法中的一种，有限内存（L-BFGS）法。它具有拟牛顿法不需要存储大型海森矩阵或它的逆矩阵的优点，同时在拟牛顿法的基础上做了改进，给定一个正整数m，只需存储前面m次的迭代信息，大大减少了计算时占用的内存空间，从而提高了计算速度。然后，设计一个两层介质的模型，通过正演计算模型的响应，对模型响应施加固定误差作为观测数据参与反演。反演过程中，改变初始模型、网格大小和频率，对比分析反演结果发现，因为L-BFGS法是在适当的条件下具有全局收敛性，所以初始模型如何选择对于反演结果影响很大。为了提高反演的效率和准确性，本次研究通过粗网格全频率反演结果设计了反演的初始模型。再根据要反演的异常深度，计算关键频率，采用精细网格部分频率反演，得到准确的反演结果。最后，本文对理论模型中提出的反演方案对实际数据进行了反演验证。根据粗网格全频率反演结果设计初始模型。根据实际需要选择反演频率，在最佳频率的基础上，加入了高频、低频和高频低频的组合，来控制上下出现的虚假异常，对比分析寻找反演的最佳频率组合。反演结果与地质资料和其他地球物理方法结果吻合较好，说明了这种反演方案的可行性。本文通过理论模型和实际数据的反演研究得出以下结论：1、提出了一种可行性的反演方案，首先根据粗网格全频率反演结果设计初始模型，然后由探测深度公式求得关键频率，加入高频和低频，初始模型选精细网格在进行一次反演。这种方案既节约了计算时间，又保证了反演的准确性。2、反演计算在选择初始模型时，初始模型电阻率如果低于实际模型电阻率，反演结果较难拟合，反演的电阻率较低。初始模型电阻率高于实际模型电阻率则能更接近于理论模型。3、三维反演过程中频率的个数不是越多越好，需要通过计算来求得关键频率，再引入高频和低频进行控制，，反演结果更为准确。4、电场Ex分量反演，在x方向上控制较好，y方向上有延伸。
[Abstract]:Controlled Source Audio Magnetotelluric Sounding (CSAMT) has become an important means of electromagnetic exploration since it came out in the 1970s and 1980s. Now, one-dimensional and two-dimensional forward and inversion research of CSAMT has become more and more mature, and three-dimensional forward and inversion research has made considerable progress. The finite element method and the integral equation method, the inversion method has the conjugate gradient method, the nonlinear conjugate gradient method, the Newton method, the quasi-Newton method and so on. But because the computation quantity is very big, occupies the memory space many and so on the restriction, still has certain distance from the practical application. Initial model and frequency are expected to be simulated by a large number of numerical simulations, and a practical solution of controllable source inversion is proposed to realize efficient 3D real data inversion without sacrificing the inversion effect.
Firstly, we use Commer's method for reference, and decompose the total electric field excited by the finite-length wire source into the background field generated by the resistivity of layered medium and the anomalous field generated by three-dimensional anomalous body. In the inversion aspect, this paper uses one of the quasi-Newton methods, the finite memory (L-BFGS) method. It has the advantage that the quasi-Newton method does not need to store the large Heisen matrix or its inverse matrix. At the same time, it is improved on the basis of the quasi-Newton method. Given a positive integer m, it only needs to store the iterative information of the previous m times, which greatly reduces the calculation. The memory space is occupied, thus improving the computation speed.
Then, a two-layer medium model is designed, and a fixed error is applied to the model response as the observed data through forward calculation. During the inversion process, the initial model, mesh size and frequency are changed. The inversion results show that L-BFGS method has global convergence under appropriate conditions, so the initial inversion is carried out. In order to improve the efficiency and accuracy of inversion, an initial inversion model is designed based on the full-frequency inversion results of coarse grids. Then the key frequency is calculated according to the anomaly depth to be inverted, and the accurate inversion results are obtained by partial frequency inversion of fine grids.
Finally, the inversion scheme proposed in the theoretical model is used to validate the actual data. The initial model is designed according to the full-frequency inversion results of the coarse grid. The inversion frequency is selected according to the actual needs. On the basis of the optimal frequency, the combination of high frequency, low frequency and high frequency low frequency is added to control the false anomalies, and the comparison is made. The inversion results are in good agreement with geological data and other geophysical methods, which shows the feasibility of this inversion scheme.
In this paper, the following conclusions are drawn through the inversion of theoretical model and actual data: 1. A feasible inversion scheme is proposed. First, the initial model is designed according to the full-frequency inversion result of coarse mesh, then the key frequency is obtained by the formula of detection depth, and the high and low frequencies are added to the initial model, and the fine mesh is selected for one inversion. This scheme not only saves calculation time, but also ensures the accuracy of inversion. 2. When selecting the initial model, if the initial model resistivity is lower than the actual model resistivity, the inversion result is more difficult to fit, and the inversion resistivity is lower. In the process of the inversion, the number of frequencies is not the more, the better. It is necessary to calculate the key frequencies, and then introduce high and low frequencies to control the inversion. 4. The inversion results of Ex component of electric field are more accurate.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.325

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